Sample quiz on equations of altitudes Main home here.

1. In a $\triangle ABC$, an altitude from vertex $A$ is $\cdots$?
a line from $A$ that bisects side $BC$ at $45^{\circ}$
a line from $A$ that meets side $BC$ at $90^{\circ}$
a line from $A$ that bisects side $BC$ at $90^{\circ}$
a line from $A$ to the midpoint of side $BC$.
2. The point of intersection of the three altitudes of a triangle is known as $\cdots$?
centroid
circumcenter
orthocenter
altocenter
3. If a triangle contains an obtuse angle, how many of its altitudes are external (outside the triangle)?
$0$
$1$
$2$
$3$
4. Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the equation of the altitude from $A$.
$y=x$
$y=-x$
$y=-\frac{1}{2}x+\frac{5}{2}$
$y=-2x+5$
5. Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the equation of the altitude from $B$.
$y=x$
$y=-x$
$y=-\frac{1}{2}x+\frac{5}{2}$
$y=-2x+5$
6. Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the equation of the altitude from $C$.
$y=x$
$y=-x$
$y=-\frac{1}{2}x+\frac{5}{2}$
$y=-2x+5$
7. Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the (coordinates of the) foot of the altitude from $C$.
$(\frac{3}{2},\frac{3}{2})$
$(\frac{2}{3},\frac{3}{2})$
$(\frac{3}{2},\frac{2}{3})$
$(\frac{2}{3},\frac{2}{3})$
8. Find the orthocenter of $\triangle ABC$ whose vertices are located at $A(1,2),~(2,1),~C(3,3)$.
$(\frac{3}{5},\frac{3}{5})$
$(\frac{5}{3},\frac{5}{3})$
$(-\frac{5}{3},\frac{5}{3})$
$(-\frac{3}{5},\frac{3}{5})$
9. Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the equation of the altitude from $A$.
$y=-x$
$y=-x+1$
$y=-\frac{1}{2}x+\frac{9}{2}$
$y=-\frac{1}{4}x+\frac{27}{4}$
10. Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the equation of the altitude from $B$.
$y=-x$
$y=-x+1$
$y=-\frac{1}{2}x+\frac{9}{2}$
$y=-\frac{1}{4}x+\frac{27}{4}$
11. Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the equation of the altitude from $C$.
$y=-x$
$y=-x+1$
$y=-\frac{1}{2}x+\frac{9}{2}$
$y=-\frac{1}{4}x+\frac{27}{4}$
12. Find the orthocenter of $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$.
$(-9,9)$
$(9,-9)$
$(9,9)$
$(0,9)$
13. Consider $\triangle ABC$ in which $\angle C=90^{\circ}$. This triangle's orthocenter is located at $\cdots$?
$A$
$B$
$C$
$AB$
14. Find the distance between the centroid and the foot of the altitude from $C$, given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$.
$1$
$2$
$\sqrt{2}$
$\frac{\sqrt{2}}{2}$
15. Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the LENGTH of the altitude from $A$.
$\frac{3}{2}$
$\frac{2}{3}$
$\frac{3}{2}\sqrt{2}$
$\frac{2}{3}\sqrt{2}$